How do I use the binomial theorem to find the constant term?

Let ##(2x+3) ^3## be a given binomial.
From the binomial expression write down the general term. Let this term be the r+1 th term. Now simplify this general term. If this general term is a constant term then it should not contain the variable x.
Let us write the general term of the above binomial.
##T_(r+1)## = ## ^3 C_r## ##(2x)^(3-r)## ##3^r##
simplifying we get ##T_(r+1)##= ## ^3 C_r## ##2^(3-r)## ##3^r## ##x^(3-r)##
Now for this term to be the constant term ##x^(3-r)## should be equal to 1.
Therefore ##x^(3-r)##= ##x^0##
=> 3-r =0
=> r=3
Thus the fourth term in the expansion is the constant term. By putting r=3 in the general term we will get the value of the constant term.